GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2018, 19:58

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

Is |x + y| > |x - y| ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 06 Feb 2013
Posts: 8
Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post Updated on: 20 Dec 2017, 20:09
2
17
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

59% (02:19) correct 41% (02:24) wrong based on 369 sessions

HideShow timer Statistics

Is |x + y| > |x - y| ?

(1) |x| > |y|
(2) |x - y| < |x|

Originally posted by josemarioamaya on 25 Sep 2013, 13:07.
Last edited by Bunuel on 20 Dec 2017, 20:09, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 25 Sep 2013, 13:18
11
8
Is |x + y| > |x - y| ?

Is \(|x+y| > |x-y|\)? --> square it: is \(x^2+2xy+y^2>x^2-2xy+y^2\) --> is \(xy>0\)?

(1) |x| > |y|. We cannot get from this whether x and y have the same sign. Not sufficient.

(2) |x - y| < |x| --> square again: \(x^2-2xy+y^2<x^2\) --> \(xy>\frac{y^2}{2}\) --> since \(y^2\geq{0}\) (the square of any number is more than or equal to 0), then we have that \(xy>\frac{y^2}{2}\geq{0}\). Sufficient.

Answer: B.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 306
Schools: Dartmouth College
Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 29 Jul 2018, 18:47
1
Mo2men wrote:
GMATGuruNY
Can you please show how I can open the modulus in statement 2 instead of squaring both sides .

Thanks


Statement 2: |x-y| < |x|

Case 1: x>0 and x≥y
In this case, |x-y| = x-y and |x| = x.
Substituting the blue equations into |x-y| < x, we get:
x-y < x
-y < 0
y > 0
Implication:
If x>0 and x≥y, then y>0.
Thus:
0<y≤x

Case 2: x>0 and x<y
In this case, |x-y| = -x+y and |x| = x.
Substituting the blue equations into |x-y| < x, we get:
-x+y < x
y < 2x
Implication:
If x>0 and x<y, then y<2x.
Thus:
0<x<y<2x

Case 3: x<0 and x≥y
In this case, |x-y| = x-y and |x| = -x.
Substituting the blue equations into |x-y| < x, we get:
x-y < -x
2x < y
Implication:
If x<0 and x≥y, then y>2x.
Thus:
2x<y≤x<0

Case 4: x<0 and x<y
In this case, |x-y| = -x+y and |x| = -x.
Substituting the blue equations into |x-y| < x, we get:
-x+y < -x
y < 0
Implication:
If x<0 and x<y, then y<0.
Thus:
x<y<0

In all four cases, x and y have the same sign, so xy>0.

I do not recommend this approach.
Squaring the inequality seems easier and faster.
_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

General Discussion
Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 29
WE: General Management (Consulting)
GMAT ToolKit User
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 26 Sep 2013, 08:16
Bunuel wrote:
Is |x + y| > |x - y| ?

Is \(|x+y| > |x-y|\)? --> square it: is \(x^2+2xy+y^2>x^2-2xy+y^2\) --> is \(xy>0\)?

(1) |x| > |y|. We cannot get from this whether x and y have the same sign. Not sufficient.

(2) |x - y| < |x| --> square again: \(x^2-2xy+y^2<x^2\) --> \(xy>\frac{y^2}{2}\) --> since \(y^2\geq{0}\) (the square of any number is more than or equal to 0), then we have that \(xy>\frac{y^2}{2}\geq{0}\). Sufficient.

Answer: B.

Hope it's clear.


Sorry Bunuel,

but i don't understand the concept behind the solution...

I understand that an absolute value is always positive. But how can you just square it¿? It supposed to be the root square of the square, isn't it¿??
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50623
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 26 Sep 2013, 08:19
jacg20 wrote:
Bunuel wrote:
Is |x + y| > |x - y| ?

Is \(|x+y| > |x-y|\)? --> square it: is \(x^2+2xy+y^2>x^2-2xy+y^2\) --> is \(xy>0\)?

(1) |x| > |y|. We cannot get from this whether x and y have the same sign. Not sufficient.

(2) |x - y| < |x| --> square again: \(x^2-2xy+y^2<x^2\) --> \(xy>\frac{y^2}{2}\) --> since \(y^2\geq{0}\) (the square of any number is more than or equal to 0), then we have that \(xy>\frac{y^2}{2}\geq{0}\). Sufficient.

Answer: B.

Hope it's clear.


Sorry Bunuel,

but i don't understand the concept behind the solution...

I understand that an absolute value is always positive. But how can you just square it¿? It supposed to be the root square of the square, isn't it¿??


If both sides of an inequality are non negative, then we can square it.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1745
Concentration: Finance
GMAT ToolKit User
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 09 May 2014, 14:25
1
I solved in the following way

First square both sides

We get 'Is xy>0" , or in proper english do 'x' and 'y' have the same sign?

Statement 1: Obviously insufficient
Statement 2: Square both sides again ---> x^2 > x^2 - 2xy + y^2

y^2 - 2xy < 0

y (y-2x)<0

So two cases:

If y>0, then y-2x<0 and 2x>y>0. Answer is YES
If y<0, then y-2x>0 and 2x<y<0. Answer is YES again

Sufficient

Answer: B
Manager
Manager
avatar
S
Joined: 27 Aug 2014
Posts: 140
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)
CAT Tests
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 04 Nov 2014, 10:05
1
Basically the question is asking if x and y have the same sign.

from statement 1: no info on signs.---NSF

for statement 2: I did the following:

The distance between x and y on the number line can be less than the distance of 0 and x only when x and y have the same sign.

---------y----x---------0--------------
or
----------0---------x---y-------------

if
------x-------0--------y---- or ---------y--------0------------x----------
then the statement-2 is not true.

Therefore x and y should have the same sign.
Answer -(b)
Director
Director
User avatar
D
Joined: 11 Feb 2015
Posts: 566
Premium Member CAT Tests
Re: Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 25 Jul 2018, 08:55
Statement 1 is insufficient when you test for positive & negative numbers. For e.g. (8,7) & (-8,7)

Statement 2 is sufficient hence Option B is the correct answer.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1880
Reviews Badge CAT Tests
Is |x + y| > |x - y| ?  [#permalink]

Show Tags

New post 27 Jul 2018, 03:29
Bunuel wrote:
Is |x + y| > |x - y| ?

Is \(|x+y| > |x-y|\)? --> square it: is \(x^2+2xy+y^2>x^2-2xy+y^2\) --> is \(xy>0\)?

(1) |x| > |y|. We cannot get from this whether x and y have the same sign. Not sufficient.

(2) |x - y| < |x| --> square again: \(x^2-2xy+y^2<x^2\) --> \(xy>\frac{y^2}{2}\) --> since \(y^2\geq{0}\) (the square of any number is more than or equal to 0), then we have that \(xy>\frac{y^2}{2}\geq{0}\). Sufficient.

Answer: B.

Hope it's clear.


GMATGuruNY
Can you please show how I can open the modulus in statement 2 instead of squaring both sides .

Thanks
GMAT Club Bot
Is |x + y| > |x - y| ? &nbs [#permalink] 27 Jul 2018, 03:29
Display posts from previous: Sort by

Is |x + y| > |x - y| ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.